Related papers: Clearing Sections of Lattice Liability Networks

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional…

The debts' clearing problem is about clearing all the debts in a group of n entities (persons, companies etc.) using a minimal number of money transaction operations. The problem is known to be NP-hard in the strong sense. As for many…

Credit networks represent a way of modeling trust between entities in a network. Nodes in the network print their own currency and trust each other for a certain amount of each other's currency. This allows the network to serve as a…

In this paper, we propose a dynamical model to capture cascading failures among interconnected organizations in the global financial system. Failures can take the form of bankruptcies, defaults, and other insolvencies. The network that…

We demonstrate using multi-layered networks, the existence of an empirical linkage between the dynamics of the financial network constructed from the market indices and the macroeconomic networks constructed from macroeconomic variables…

Evaluation of systemic risk in networks of financial institutions in general requires information of inter-institution financial exposures. In the framework of Debt Rank algorithm, we introduce an approximate method of systemic risk…

We study financial networks with debt contracts and credit default swaps between specific pairs of banks. Given such a financial system, we want to decide which of the banks are in default, and how much of their liabilities can these…

Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

We consider networks of banks with assets and liabilities. Some banks may be insolvent, and a central bank can decide which insolvent banks, if any, to bail out. We view bailouts as an optimization problem where the central bank has given…

To understand the controllability of complex networks is a forefront problem relevant to different fields of science and engineering. Despite recent advances in network controllability theories, an outstanding issue is to understand the…

We propose a unified mathematical framework for classifying phases of matter. The framework is based on different types of combinatorial structures with a notion of locality called lattices. A tensor lattice is a local prescription that…

We describe a novel family of models of multi- layer feedforward neural networks in which the activation functions are encoded via penalties in the training problem. Our approach is based on representing a non-decreasing activation function…

A fundamental problem in studying and modeling economic and financial systems is represented by privacy issues, which put severe limitations on the amount of accessible information. Here we introduce a novel, highly nontrivial method to…

Current post-trade clearing systems rely almost exclusively on cash or cash-like collateral, leaving vast reserves of short-term liquidity embedded in trade credit outside formal settlement infrastructures. A key barrier to integrating this…

Eisenberg and Noe (2001) analyze systemic risk for financial institutions linked by a network of liabilities. They show that the solution to their model is unique when the financial system is satisfies a regularity condition involving risk…

The scope of financial systemic risk research encompasses a wide range of interbank channels and effects, including asset correlation shocks, default contagion, illiquidity contagion, and asset fire sales. This paper introduces a financial…

We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared…

In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…